Question: Rewrite as a simplified fraction. ${3.7\overline{2} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 372.2222...\\ 10x &= 37.2222...\end{align*}}$ Subtracting the two equations, we have: ${90x = 335}$ ${x = \dfrac{335}{90}} $ ${x = \dfrac{67}{18}} \text{or} {3 \dfrac{13}{18}}$